Just remove the credit card from the account and let them suspend it indefinitely. Beware that you will lose anything you had stored on the account.
If you really need Amazon, set up a new account with a new email address, although I'd stay away from AWS.
Just make sure to store any emails and support protocols that indicate that the account was recognized as hacked. This will be important if you ever have to deal with the debt in mediation/court.
Signing up again under a different name to continue using the service you have been banned from could be considered fraud by misrepresentation, which in most places is a fairly serious criminal offence (even though it is very unlikely to be prosecuted in this case).